5. A uniform solid right circular cone has height \(h\) and base radius \(r\). The top part of the cone is removed by cutting through the cone parallel to the base at a height \(\frac { h } { 2 }\).

1. Show that the centre of mass of the remaining solid is at a height
   \(\frac { 11 h } { 56 }\) above the base, along its axis of symmetry. The remaining part of the solid is suspended from the point \(D\) on the circumference of its smaller circular face, and the axis of symmetry then makes an angle \(\alpha\) with the vertical, where \(\tan \alpha = \frac { 1 } { 2 }\).
2. Find the value of the ratio \(h : r\).